11 citations · 33 across the 13 of their papers we have counts for
14 papers
The equality case in Godbersen's inequality and its generalizations
Omer Friedland, Eli Putterman, Maud Szusterman
Godbersen's long-standing conjecture states that the mixed volumes of any convex body satisfy for a…
Sharp stability for the (B)-theorem
Eli Putterman
The (B)-theorem of Cordero-Erausquin, Fradelizi and Maurey states that if is the standard Gaussian in , is an origin-symmetric convex set,…
On the polar of Schneider's difference body
Julián Haddad, Dylan Langharst, Galyna V. Livshyts +1
In 1970, Schneider introduced the th-order extension of the difference body of a convex body , the convex body in . He conject…
On unbalanced difference bodies and Godbersen's conjecture
Shiri Artstein-Avidan, Eli Putterman
The longstanding Godbersen's conjecture states that for any convex body of volume and any , the mixed volume $V_j = V(K[j], -K[n…
On the Variance, Admissibility, and Stability of Empirical Risk Minimization
Gil Kur, Eli Putterman, Alexander Rakhlin
It is well known that Empirical Risk Minimization (ERM) may attain minimax suboptimal rates in terms of the mean squared error (Birgé and Massart, 1993). In this paper, we prove th…
Higher-Order Lp Isoperimetric and Sobolev Inequalities
Julián Haddad, Dylan Langharst, Eli Putterman +2
Schneider introduced an inter-dimensional difference body operator on convex bodies and proved an associated inequality. In the prequel to this work, we showed that this concept ca…
On the -Order Weighted Projection Body Operator and Related Inequalities
Dylan Langharst, Eli Putterman, Michael Roysdon +1
For a convex body in , the inequalities of Rogers-Shephard and Zhang, written succinctly, are $$\text{vol}_n(DK)\leq \binom{2n}{n} \text{vol}_n(K) \leq \text{vol}_…
Affine Isoperimetric Inequalities for Higher-Order Projection and Centroid Bodies
Julián Haddad, Dylan Langharst, Eli Putterman +2
In 1970, Schneider introduced the th order difference body of a convex body, and also established the th-order Rogers-Shephard inequality. In this paper, we extend this idea…
An Efficient Minimax Optimal Estimator For Multivariate Convex Regression
Gil Kur, Eli Putterman
This work studies the computational aspects of multivariate convex regression in dimensions . Our results include the \emph{first} estimators that are minimax optimal (up…
Some new positions of maximal volume of convex bodies
Shiri Artstein-Avidan, Eli Putterman
In this paper, we extend and generalize several previous works on maximal-volume positions of convex bodies. First, we analyze the maximal positive-definite image of one convex bod…
Spectral monotonicity under Gaussian convolution
Bo'az Klartag, Eli Putterman
We show that the Poincaré constant of a log-concave measure in Euclidean space is monotone increasing along the heat flow. In fact, the entire spectrum of the associated Laplace op…
Cubature formulas and Sobolev inequalities
Eli Putterman
We study a problem in the theory of cubature formulas on the sphere: given , determine the infimum of over cubature formulas of str…
Equivalence of the local and global versions of the -Brunn-Minkowski inequality
Eli Putterman
By studying -combinations of strongly isomorphic polytopes, we prove the equivalence of the -Brunn-Minkowski inequality conjectured by Böröczky, Lutwak, Yang and Zhang to…
The Square Cat
E. Putterman, O. Raz
We present a simple, two dimensional example of a "cat" -- a body with zero angular momentum that can rotate itself with no external forces. This model is used to explain why this…